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Question
If `|veca| = 3, |vecb| = sqrt(2)/3` and `veca xx vecb` is a unit vector then the angle between `veca` and `vecb` will be ______.
Options
`π/6`
`π/4`
`π/3`
`π/2`
Solution
If `|veca| = 3, |vecb| = sqrt(2)/3` and `veca xx vecb` is a unit vector then the angle between `veca` and `vecb` will be `underlinebb(π/4)`.
Explanation:
Given `veca xx vecb` is a unit vector,
∴ `|veca xx vecb|` = 1
∵ `|veca xx vecb| = |veca||vecb| sin θ`
1 = `3 xx sqrt(2)/3 sin θ`
`\implies` sin θ = `1/sqrt(2)`
= `sin π/4`
`\implies` θ = `π/4`
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